Answer:
AI-generated answer
To find the values of m and n, we can consider the following steps:
1. Understand the given information:
We are given that [m n] [m] = [1 3] and m + 1 = n.
2. Understand matrix multiplication:
In matrix multiplication, the element in the i-th row and j-th column of the resulting matrix is found by multiplying the corresponding elements of the i-th row of the first matrix with the j-th column of the second matrix and summing the products.
3. Write the equation for matrix multiplication:
[m n] [m] = [1 3]
4. Apply matrix multiplication:
The resulting matrix will have one row and one column, so we can simplify the equation to:
m * m + n * 1 = 1
This simplifies to:
m^2 + n = 1
5. Substitute the value of n:
Since m + 1 = n, we can substitute this into the equation:
m^2 + (m + 1) = 1
6. Simplify the equation and solve for m:
m^2 + m + 1 = 1
m^2 + m = 0
m(m + 1) = 0
7. Find the values of m and n:
From the equation m(m + 1) = 0, we have two possibilities:
m = 0 or m + 1 = 0
If m = 0, then n = m + 1 = 0 + 1 = 1.
If m + 1 = 0, then m = -1 and n = m + 1 = -1 + 1 = 0.
Therefore, the possible values for m and n are:
m = 0, n = 1
or
m = -1, n = 0.
Explanation: